Question

If you double the length of a rectangle and leave the width the same, how does the area and perimeter change?

Answer 1

The new perimeter will be (old perimeter) + 2(old length) or 2(2l+b). The new area will be twice the old area.

Answer 2

let the original length be x unit and width be y unit.

Original Area = x*y sq.unit = xy sq.unit
Original Perimeter = 2(x+y) unit = 2x+2y

New length = 2x
New width = y
Area = 2x*y sq.unit = 2xy sq.unit
Perimeter = 2(2x+y) unit = 4x+2y unit

Increase in Area = (2xy - xy) = xy sq.unit
Increase in Perimeter = (4x+2y) - (2x+2y)
= 2x unit

Ans) The Area of rectangle gets doubled and Perimeter increases by twice the length of the Rectangle when length of the Rectangle is doubled.